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Australian Optical Society
Photonic bandgaps in woodpile structures
G. H. SMITH, L. C. BOTTEN1, R. C. MCPHEDRAN2 AND N. A. NICOROVICI1,2.
1
Department of Mathematical Sciences, University of Technology, Sydney, Broadway, NSW 2007,
Australia
2
School of Physics, University of Sydney, NSW 2006, Australia
Three-dimensional photonic band gap structures are the ultimate goal for photonic crystals as, unlike one
and two-dimensional crystals, they provide for total confinement. One such configuration is the woodpile
structure, consisting of layers of dielectric rods with a stacking
sequence, which repeats itself every four layers.
Our method involves the formulation of plane wave scattering
matrices for the structure, derived recursively from the
scattering matrices of its component layers, using a Rayleigh
method, in which the field quantities are written as multipole
expansions. For each layer, there is dispersion in only one
direction and thus the 2D-diffraction problem is characterised
by a family of 1D problems. Each problem is associated with
incidence parameters corresponding to the diffracted orders of
the orthogonal grating, leading to scattering matrices that are
block diagonal or some permutation thereof.
The theory is applied to deduce the spectral properties of the
woodpile layering, band diagrams for woodpile photonic
crystals, transmission spectra and field plots.
Two dimensional projection of the band structure of a
woodpile crystal, showing a total band gap. The
cylindrical rods have a radius of 0.09 and a refractive
index of 3.6. The rods within each layer are separated by
0.65. The distance between layers is 0.22.
While the theory we have developed applies to a structure
based on cylindrical gratings, it is readily extensible to the structures based on lamellar gratings of
rectangular cross-section that are being fabricated by, for example, Sandia Laboratories.